Exact quantization of superconducting circuits

Circuits consisting of weak anharmonic qubits coupled to cavity multimodes are theoretically quatized beyond dispersive regime. In order to do this, we obtain a unitary transformation that diagonalizes harmonic sector of the circuit. Weak anharmonicity does not alter normal mode basis, however it modifies energy levels. using our formalism we we quantize two circuits of 1) a transmon coupled to a resonator, and 2) two transmons coupled to a bus resonator. In both circuits we determine dressed frequencies and Kerr nonlinearities in closed form formulas. Our results are valid for arbitrary frequency detuning and coupling within and beyond dispersive regime.

Reference: MH. Ansari, arXiv:1807.00792